Home Explore Help
Register Sign In
xiaojincai
/
docxconvert
Watch 1
Star 0
Fork 0
Files Issues 0 Pull Requests 0 Wiki
Tree: 9cdb19a286
Branches Tags
docxconvert
/
test4.html

test4.html 41 KB
History Raw

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690691692693694695696697698699700701702703 
  1. <html>
    2. 

  2. 

  3. <head>
    4. 

  4. <meta http-equiv=Content-Type content="text/html; charset=gb2312">
    5. 

  5. <meta name=Generator content="Microsoft Word 15 (filtered)">
    6. 

  6. <style>
    7. 

  7. <!--
    8. 

  8.  /* Font Definitions */
    9. 

  9.  @font-face
    10. 

  10. 	{font-family:宋体;
    11. 

  11. 	panose-1:2 1 6 0 3 1 1 1 1 1;}
    12. 

  12. @font-face
    13. 

  13. 	{font-family:黑体;
    14. 

  14. 	panose-1:2 1 6 9 6 1 1 1 1 1;}
    15. 

  15. @font-face
    16. 

  16. 	{font-family:"Cambria Math";
    17. 

  17. 	panose-1:2 4 5 3 5 4 6 3 2 4;}
    18. 

  18. @font-face
    19. 

  19. 	{font-family:Calibri;
    20. 

  20. 	panose-1:2 15 5 2 2 2 4 3 2 4;}
    21. 

  21. @font-face
    22. 

  22. 	{font-family:"\@黑体";
    23. 

  23. 	panose-1:2 1 6 9 6 1 1 1 1 1;}
    24. 

  24. @font-face
    25. 

  25. 	{font-family:"\@宋体";
    26. 

  26. 	panose-1:2 1 6 0 3 1 1 1 1 1;}
    27. 

  27.  /* Style Definitions */
    28. 

  28.  p.MsoNormal, li.MsoNormal, div.MsoNormal
    29. 

  29. 	{margin:0cm;
    30. 

  30. 	margin-bottom:.0001pt;
    31. 

  31. 	text-align:justify;
    32. 

  32. 	text-justify:inter-ideograph;
    33. 

  33. 	font-size:10.5pt;
    34. 

  34. 	font-family:"Times New Roman","serif";}
    35. 

  35. p.MsoHeader, li.MsoHeader, div.MsoHeader
    36. 

  36. 	{mso-style-link:"页眉 Char";
    37. 

  37. 	margin:0cm;
    38. 

  38. 	margin-bottom:.0001pt;
    39. 

  39. 	text-align:center;
    40. 

  40. 	layout-grid-mode:char;
    41. 

  41. 	border:none;
    42. 

  42. 	padding:0cm;
    43. 

  43. 	font-size:9.0pt;
    44. 

  44. 	font-family:"Times New Roman","serif";}
    45. 

  45. p.MsoFooter, li.MsoFooter, div.MsoFooter
    46. 

  46. 	{mso-style-link:"页脚 Char";
    47. 

  47. 	margin:0cm;
    48. 

  48. 	margin-bottom:.0001pt;
    49. 

  49. 	layout-grid-mode:char;
    50. 

  50. 	font-size:9.0pt;
    51. 

  51. 	font-family:"Times New Roman","serif";}
    52. 

  52. p.MsoAcetate, li.MsoAcetate, div.MsoAcetate
    53. 

  53. 	{mso-style-link:"批注框文本 Char";
    54. 

  54. 	margin:0cm;
    55. 

  55. 	margin-bottom:.0001pt;
    56. 

  56. 	text-align:justify;
    57. 

  57. 	text-justify:inter-ideograph;
    58. 

  58. 	font-size:9.0pt;
    59. 

  59. 	font-family:"Times New Roman","serif";}
    60. 

  60. p.MsoNoSpacing, li.MsoNoSpacing, div.MsoNoSpacing
    61. 

  61. 	{mso-style-link:"无间隔 Char";
    62. 

  62. 	margin:0cm;
    63. 

  63. 	margin-bottom:.0001pt;
    64. 

  64. 	font-size:11.0pt;
    65. 

  65. 	font-family:"Times New Roman","serif";}
    66. 

  66. span.Char
    67. 

  67. 	{mso-style-name:"页眉 Char";
    68. 

  68. 	mso-style-link:页眉;}
    69. 

  69. span.Char0
    70. 

  70. 	{mso-style-name:"页脚 Char";
    71. 

  71. 	mso-style-link:页脚;}
    72. 

  72. span.Char1
    73. 

  73. 	{mso-style-name:"批注框文本 Char";
    74. 

  74. 	mso-style-link:批注框文本;}
    75. 

  75. span.Char2
    76. 

  76. 	{mso-style-name:"无间隔 Char";
    77. 

  77. 	mso-style-link:无间隔;}
    78. 

  78.  /* Page Definitions */
    79. 

  79.  @page WordSection1
    80. 

  80. 	{size:21.0cm 841.95pt;
    81. 

  81. 	margin:72.0pt 54.0pt 72.0pt 54.0pt;
    82. 

  82. 	layout-grid:15.6pt;}
    83. 

  83. div.WordSection1
    84. 

  84. 	{page:WordSection1;}
    85. 

  85. -->
    86. 

  86. </style>
    87. 

  87. 

  88. </head>
    89. 

  89. 

  90. <body lang=ZH-CN style='text-justify-trim:punctuation'>
    91. 

  91. 

  92. <div class=WordSection1 style='layout-grid:15.6pt'>
    93. 

  93. 

  94. <p class=MsoNormal align=center style='text-align:center'><b><span lang=EN-US
    95. 

  95. style='font-size:15.0pt'>2020-2021</span></b><b><span style='font-size:15.0pt;
    96. 

  96. font-family:黑体'>学年度高中数学期中考试卷</span></b></p>
    97. 

  97. 

  98. <p class=MsoNormal align=center style='text-align:center'><b><span
    99. 

  99. style='font-size:18.0pt;font-family:黑体'>试卷副标题</span></b></p>
    100. 

  100. 

  101. <p class=MsoNormal><span lang=EN-US>&nbsp;</span></p>
    102. 

  102. 

  103. <p class=MsoNormal align=center style='text-align:center'><b><span
    104. 

  104. style='font-size:12.0pt;font-family:宋体'>第<span lang=EN-US>I</span>卷（选择题）</span></b></p>
    105. 

  105. 

  106. <p class=MsoNormal><span lang=EN-US>&nbsp;</span></p>
    107. 

  107. 

  108. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题型】</span></b><b><span
    109. 

  109. style='font-family:宋体'>一、单选题</span></b></p>
    110. 

  110. 

  111. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    112. 

  112. 

  113. <p class=MsoNormal><b><span lang=EN-US>1</span></b><b><span style='font-family:
    114. 

  114. 宋体'>、设集合</span><span lang=EN-US><img width=121 height=29
    115. 

  115. src="test4.files/image001.png" alt=eqIdb520b5dfe5764b2e98b4e921739bbc3f></span></b><b><span
    116. 

  116. style='font-family:宋体'>，</span><span lang=EN-US><img width=120 height=27
    117. 

  117. src="test4.files/image002.png" alt=eqId5d6adef459e04df38a33fc5c16a2e665></span></b><b><span
    118. 

  118. style='font-family:宋体'>，则</span><span lang=EN-US><img width=54 height=20
    119. 

  119. src="test4.files/image003.png" alt=eqId170a03e31a0e4656b66452088e998e61></span></b><b><span
    120. 

  120. style='font-family:宋体'>（</span><span lang=EN-US>&nbsp;&nbsp;&nbsp; </span></b><b><span
    121. 

  121. style='font-family:宋体'>）</span></b></p>
    122. 

  122. 

  123. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    124. 

  124. vertical-align:middle'><b><span lang=EN-US>A</span></b><b><span
    125. 

  125. style='font-family:宋体'>．</span><span lang=EN-US><img width=92 height=29
    126. 

  126. src="test4.files/image004.png" alt=eqId1015e0ea95614d9fa144f2f1167ac38c>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; B</span></b><b><span
    127. 

  127. style='font-family:宋体'>．</span><span lang=EN-US><img width=88 height=32
    128. 

  128. src="test4.files/image005.png" alt=eqIde2383d62764744db8cf4a995f1b93623></span></b></p>
    129. 

  129. 

  130. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    131. 

  131. vertical-align:middle'><b><span lang=EN-US>C</span></b><b><span
    132. 

  132. style='font-family:宋体'>．</span><span lang=EN-US><img width=80 height=27
    133. 

  133. src="test4.files/image006.png" alt=eqIdd35379a2dc934bc8974792df4ce5d6fb>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; D</span></b><b><span
    134. 

  134. style='font-family:宋体'>．</span><span lang=EN-US><img width=88 height=27
    135. 

  135. src="test4.files/image007.png" alt=eqId34c9dac3d6344ff39fbb423fd6c08402></span></b></p>
    136. 

  136. 

  137. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    138. 

  138. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b><b><span
    139. 

  139. style='font-family:宋体'>集合的概念及运算</span></b></p>
    140. 

  140. 

  141. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    142. 

  142. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    143. 

  143. 

  144. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    145. 

  145. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    146. 

  146. lang=EN-US>C</span></p>
    147. 

  147. 

  148. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    149. 

  149. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【解析】</span></b></p>
    150. 

  150. 

  151. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    152. 

  152. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    153. 

  153. lang=EN-US>]</span><span style='font-family:宋体'>根据集合交集运算求解即可得答案</span><span
    154. 

  154. lang=EN-US>.</span></p>
    155. 

  155. 

  156. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    157. 

  157. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    158. 

  158. lang=EN-US>]</span></p>
    159. 

  159. 

  160. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    161. 

  161. vertical-align:middle'><span style='font-family:宋体'>解：</span><span lang=EN-US><img
    162. 

  162. width=343 height=29 src="test4.files/image008.png"
    163. 

  163. alt=eqIdf2c66b848a8e4b969f7e3059790e94ad></span></p>
    164. 

  164. 

  165. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    166. 

  166. vertical-align:middle'><span style='font-family:宋体'>故选：</span><span lang=EN-US>C</span></p>
    167. 

  167. 

  168. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    169. 

  169. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    170. 

  170. 

  171. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    172. 

  172. vertical-align:middle'><b><span lang=EN-US>2</span></b><b><span
    173. 

  173. style='font-family:宋体'>、设</span><span lang=EN-US><img width=44 height=19
    174. 

  174. src="test4.files/image009.png" alt=eqId16b2d18d734d4c27ae5ae88337af4dfb></span></b><b><span
    175. 

  175. style='font-family:宋体'>，命题</span><span lang=EN-US>“</span></b><b><span
    176. 

  176. style='font-family:宋体'>存在</span><span lang=EN-US><img width=40 height=19
    177. 

  177. src="test4.files/image010.png" alt=eqId6a13e7b7d92849eba6c91758c54a673f></span></b><b><span
    178. 

  178. style='font-family:宋体'>，使方程</span><span lang=EN-US><img width=92 height=21
    179. 

  179. src="test4.files/image011.png" alt=eqId71049a1d97c54597b4593be5a686a5f4></span></b><b><span
    180. 

  180. style='font-family:宋体'>有实根</span><span lang=EN-US>”</span></b><b><span
    181. 

  181. style='font-family:宋体'>的否定是（</span><span lang=EN-US>&nbsp;&nbsp;&nbsp; </span></b><b><span
    182. 

  182. style='font-family:宋体'>）</span></b></p>
    183. 

  183. 

  184. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    185. 

  185. vertical-align:middle'><b><span lang=EN-US>A</span></b><b><span
    186. 

  186. style='font-family:宋体'>．对</span><span lang=EN-US><img width=51 height=19
    187. 

  187. src="test4.files/image012.png" alt=eqId122e29735933440ea21f70b04529083f></span></b><b><span
    188. 

  188. style='font-family:宋体'>，方程</span><span lang=EN-US><img width=92 height=21
    189. 

  189. src="test4.files/image011.png" alt=eqId71049a1d97c54597b4593be5a686a5f4></span></b><b><span
    190. 

  190. style='font-family:宋体'>无实根</span><span lang=EN-US> B</span></b><b><span
    191. 

  191. style='font-family:宋体'>．对</span><span lang=EN-US><img width=51 height=19
    192. 

  192. src="test4.files/image012.png" alt=eqId122e29735933440ea21f70b04529083f></span></b><b><span
    193. 

  193. style='font-family:宋体'>，方程</span><span lang=EN-US><img width=92 height=21
    194. 

  194. src="test4.files/image011.png" alt=eqId71049a1d97c54597b4593be5a686a5f4></span></b><b><span
    195. 

  195. style='font-family:宋体'>有实根</span></b></p>
    196. 

  196. 

  197. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    198. 

  198. vertical-align:middle'><b><span lang=EN-US>C</span></b><b><span
    199. 

  199. style='font-family:宋体'>．对</span><span lang=EN-US><img width=52 height=18
    200. 

  200. src="test4.files/image013.png" alt=eqId69a838f1f5954922969cb61f2e5d5099></span></b><b><span
    201. 

  201. style='font-family:宋体'>，方程</span><span lang=EN-US><img width=92 height=21
    202. 

  202. src="test4.files/image011.png" alt=eqId71049a1d97c54597b4593be5a686a5f4></span></b><b><span
    203. 

  203. style='font-family:宋体'>无实根</span><span lang=EN-US> D</span></b><b><span
    204. 

  204. style='font-family:宋体'>．对</span><span lang=EN-US><img width=52 height=18
    205. 

  205. src="test4.files/image013.png" alt=eqId69a838f1f5954922969cb61f2e5d5099></span></b><b><span
    206. 

  206. style='font-family:宋体'>，方程</span><span lang=EN-US><img width=92 height=21
    207. 

  207. src="test4.files/image011.png" alt=eqId71049a1d97c54597b4593be5a686a5f4></span></b><b><span
    208. 

  208. style='font-family:宋体'>有实根</span></b></p>
    209. 

  209. 

  210. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    211. 

  211. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b><b><span
    212. 

  212. style='font-family:宋体'>特称命题的否定及其真假</span></b></p>
    213. 

  213. 

  214. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    215. 

  215. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    216. 

  216. 

  217. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    218. 

  218. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    219. 

  219. lang=EN-US>A</span></p>
    220. 

  220. 

  221. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    222. 

  222. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【解析】</span></b></p>
    223. 

  223. 

  224. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    225. 

  225. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    226. 

  226. lang=EN-US>]</span></p>
    227. 

  227. 

  228. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    229. 

  229. vertical-align:middle'><span style='font-family:宋体'>只需将</span><span lang=EN-US>“</span><span
    230. 

  230. style='font-family:宋体'>存在</span><span lang=EN-US>”</span><span
    231. 

  231. style='font-family:宋体'>改成</span><span lang=EN-US>“</span><span
    232. 

  232. style='font-family:宋体'>任意</span><span lang=EN-US>”</span><span
    233. 

  233. style='font-family:宋体'>，有实根改成无实根即可</span><span lang=EN-US>.</span></p>
    234. 

  234. 

  235. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    236. 

  236. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    237. 

  237. lang=EN-US>]</span></p>
    238. 

  238. 

  239. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    240. 

  240. vertical-align:middle'><span style='font-family:宋体'>由特称命题的否定是全称命题，知</span><span
    241. 

  241. lang=EN-US>“</span><span style='font-family:宋体'>存在</span><span lang=EN-US><img
    242. 

  242. width=40 height=19 src="test4.files/image010.png"
    243. 

  243. alt=eqId6a13e7b7d92849eba6c91758c54a673f></span><span style='font-family:宋体'>，使方程</span><span
    244. 

  244. lang=EN-US><img width=92 height=21 src="test4.files/image011.png"
    245. 

  245. alt=eqId71049a1d97c54597b4593be5a686a5f4></span><span style='font-family:宋体'>有实根</span><span
    246. 

  246. lang=EN-US>”</span><span style='font-family:宋体'>的否定是</span></p>
    247. 

  247. 

  248. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    249. 

  249. vertical-align:middle'><span style='font-family:宋体'>对</span><span lang=EN-US><img
    250. 

  250. width=51 height=19 src="test4.files/image012.png"
    251. 

  251. alt=eqId122e29735933440ea21f70b04529083f></span><span style='font-family:宋体'>，方程</span><span
    252. 

  252. lang=EN-US><img width=92 height=21 src="test4.files/image011.png"
    253. 

  253. alt=eqId71049a1d97c54597b4593be5a686a5f4></span><span style='font-family:宋体'>无实根</span></p>
    254. 

  254. 

  255. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    256. 

  256. vertical-align:middle'><span style='font-family:宋体'>故选：</span><span lang=EN-US>A</span></p>
    257. 

  257. 

  258. <p class=MsoNormal><span lang=EN-US>&nbsp;</span></p>
    259. 

  259. 

  260. <p class=MsoNormal align=center style='text-align:center'><b><span
    261. 

  261. style='font-size:12.0pt;font-family:宋体'>第<span lang=EN-US>II</span>卷（非选择题）</span></b></p>
    262. 

  262. 

  263. <p class=MsoNormal><span lang=EN-US>&nbsp;</span></p>
    264. 

  264. 

  265. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题型】</span></b><b><span
    266. 

  266. style='font-family:宋体'>二、填空题</span></b></p>
    267. 

  267. 

  268. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    269. 

  269. 

  270. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    271. 

  271. vertical-align:middle'><b><span lang=EN-US>5</span></b><b><span
    272. 

  272. style='font-family:宋体'>、已知函数</span><span lang=EN-US><img width=135 height=27
    273. 

  273. src="test4.files/image014.png" alt=eqId9b7e6ad9d5394f2eae7ec51efb547299></span></b><b><span
    274. 

  274. style='font-family:宋体'>，则</span><span lang=EN-US><img width=57 height=27
    275. 

  275. src="test4.files/image015.png" alt=eqId129a6ac44fa54377a790c35febbb97c9>______</span></b><b><span
    276. 

  276. style='font-family:宋体'>．</span></b></p>
    277. 

  277. 

  278. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    279. 

  279. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b></p>
    280. 

  280. 

  281. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    282. 

  282. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    283. 

  283. 

  284. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    285. 

  285. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    286. 

  286. lang=EN-US><img width=36 height=19 src="test4.files/image016.png"
    287. 

  287. alt=eqIdc41d96c6f7194cbb8c19add37316dadc></span></p>
    288. 

  288. 

  289. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    290. 

  290. vertical-align:middle'><span style='font-family:宋体;color:red'>【<b>解析</b>】</span></p>
    291. 

  291. 

  292. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    293. 

  293. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    294. 

  294. lang=EN-US>]</span></p>
    295. 

  295. 

  296. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    297. 

  297. vertical-align:middle'><span style='font-family:宋体'>先对函数求导，然后代值计算即可</span></p>
    298. 

  298. 

  299. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    300. 

  300. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    301. 

  301. lang=EN-US>]</span></p>
    302. 

  302. 

  303. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    304. 

  304. vertical-align:middle'><span style='font-family:宋体'>解：由</span><span lang=EN-US><img
    305. 

  305. width=135 height=27 src="test4.files/image014.png"
    306. 

  306. alt=eqId9b7e6ad9d5394f2eae7ec51efb547299></span><span style='font-family:宋体'>，得</span><span
    307. 

  307. lang=EN-US><img width=133 height=27 src="test4.files/image017.png"
    308. 

  308. alt=eqId3b901e1868704d748e91a3fbfdb258b1></span><span style='font-family:宋体'>，</span></p>
    309. 

  309. 

  310. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    311. 

  311. vertical-align:middle'><span style='font-family:宋体'>所以</span><span lang=EN-US><img
    312. 

  312. width=252 height=27 src="test4.files/image018.png"
    313. 

  313. alt=eqId5bfbdf781ed447f8ab6cd8b5281de3d0></span><span style='font-family:宋体'>，</span></p>
    314. 

  314. 

  315. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    316. 

  316. vertical-align:middle'><span style='font-family:宋体'>故答案为：</span><span
    317. 

  317. lang=EN-US>2021</span></p>
    318. 

  318. 

  319. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    320. 

  320. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    321. 

  321. 

  322. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    323. 

  323. vertical-align:middle'><b><span lang=EN-US>6</span></b><b><span
    324. 

  324. style='font-family:宋体'>、设</span><span lang=EN-US><img width=13 height=15
    325. 

  325. src="test4.files/image019.png" alt=eqIda9cd3f94eb8045438f75e9daccfa7200></span></b><b><span
    326. 

  326. style='font-family:宋体'>，</span><span lang=EN-US><img width=14 height=17
    327. 

  327. src="test4.files/image020.png" alt=eqId072d7d6b911b42bc89207e72515ebf5f></span></b><b><span
    328. 

  328. style='font-family:宋体'>满足约束条件</span><span lang=EN-US><img width=100 height=48
    329. 

  329. src="test4.files/image021.png" alt=eqId967eaa5f31a04c23bd709202b104fd5f></span></b><b><span
    330. 

  330. style='font-family:宋体'>，则</span><span lang=EN-US><img width=68 height=21
    331. 

  331. src="test4.files/image022.png" alt=eqId2fe9c282900245c8a3d71f858046c892></span></b><b><span
    332. 

  332. style='font-family:宋体'>的最小值为</span><span lang=EN-US>___________.</span></b></p>
    333. 

  333. 

  334. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    335. 

  335. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b></p>
    336. 

  336. 

  337. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    338. 

  338. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    339. 

  339. 

  340. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    341. 

  341. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    342. 

  342. lang=EN-US><img width=20 height=17 src="test4.files/image023.png"
    343. 

  343. alt=eqId1d18010fc29e4f45abaaece953793246></span></p>
    344. 

  344. 

  345. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    346. 

  346. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【解析】</span></b></p>
    347. 

  347. 

  348. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    349. 

  349. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    350. 

  350. lang=EN-US>]</span></p>
    351. 

  351. 

  352. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    353. 

  353. vertical-align:middle'><span style='font-family:宋体'>作出可行域，作出目标函数对应的直线，平移该直线可得最优解．</span></p>
    354. 

  354. 

  355. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    356. 

  356. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    357. 

  357. lang=EN-US>]</span></p>
    358. 

  358. 

  359. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    360. 

  360. vertical-align:middle'><span style='font-family:宋体'>解：作出可行域，如图阴影部分，作直线</span><span
    361. 

  361. lang=EN-US><img width=68 height=21 src="test4.files/image024.png"
    362. 

  362. alt=eqId6219c25b80844355984283f98d485885></span><span style='font-family:宋体'>，由</span><span
    363. 

  363. lang=EN-US><img width=68 height=21 src="test4.files/image022.png"
    364. 

  364. alt=eqId2fe9c282900245c8a3d71f858046c892></span><span style='font-family:宋体'>得</span><span
    365. 

  365. lang=EN-US><img width=85 height=42 src="test4.files/image025.png"
    366. 

  366. alt=eqId404a472846ac46ebb230f6f31dba6071></span><span style='font-family:宋体'>，知直线向上平移时，</span><span
    367. 

  367. lang=EN-US><img width=13 height=13 src="test4.files/image026.png"
    368. 

  368. alt=eqId398ea873261745e592e97a87f920f10e></span><span style='font-family:宋体'>减小，平移直线</span><span
    369. 

  369. lang=EN-US><img width=68 height=21 src="test4.files/image024.png"
    370. 

  370. alt=eqId6219c25b80844355984283f98d485885></span><span style='font-family:宋体'>，如图所示，它过</span><span
    371. 

  371. lang=EN-US><img width=51 height=27 src="test4.files/image027.png"
    372. 

  372. alt=eqIdf2ecd79e0b494262b68113842b14bc89></span><span style='font-family:宋体'>时</span><span
    373. 

  373. lang=EN-US><img width=13 height=13 src="test4.files/image026.png"
    374. 

  374. alt=eqId398ea873261745e592e97a87f920f10e></span><span style='font-family:宋体'>取得最小值，</span><span
    375. 

  375. lang=EN-US><img width=13 height=13 src="test4.files/image026.png"
    376. 

  376. alt=eqId398ea873261745e592e97a87f920f10e></span><span style='font-family:宋体'>的最小值是</span><span
    377. 

  377. lang=EN-US><img width=20 height=17 src="test4.files/image023.png"
    378. 

  378. alt=eqId1d18010fc29e4f45abaaece953793246>.</span></p>
    379. 

  379. 

  380. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    381. 

  381. vertical-align:middle'><span style='font-family:宋体'>故答案为：</span><span
    382. 

  382. lang=EN-US><img width=20 height=17 src="test4.files/image023.png"
    383. 

  383. alt=eqId1d18010fc29e4f45abaaece953793246></span><span style='font-family:宋体'>．</span></p>
    384. 

  384. 

  385. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    386. 

  386. vertical-align:middle'><span lang=EN-US><img width=293 height=263 id="图片 100004"
    387. 

  387. src="test4.files/image028.png" alt=figure></span></p>
    388. 

  388. 

  389. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    390. 

  390. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    391. 

  391. 

  392. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    393. 

  393. vertical-align:middle'><b><span lang=EN-US>7</span></b><b><span
    394. 

  394. style='font-family:宋体'>、某歌手电视大奖赛中，七位评委对某选手打出如下分数：</span><span lang=EN-US><img
    395. 

  395. width=173 height=21 src="test4.files/image029.png"
    396. 

  396. alt=eqIdebb7f637a5de4d8cba09ed07de787983></span></b><b><span style='font-family:
    397. 

  397. 宋体'>，则其</span><span lang=EN-US><img width=20 height=19
    398. 

  398. src="test4.files/image030.png" alt=eqIdd6c0e3ca15b3431487f3ef7f69c1d8a5></span></b><b><span
    399. 

  399. style='font-family:宋体'>百分位数为</span><span lang=EN-US>________</span></b><b><span
    400. 

  400. style='font-family:宋体'>．</span></b></p>
    401. 

  401. 

  402. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    403. 

  403. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b></p>
    404. 

  404. 

  405. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    406. 

  406. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    407. 

  407. 

  408. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    409. 

  409. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    410. 

  410. lang=EN-US><img width=24 height=19 src="test4.files/image031.png"
    411. 

  411. alt=eqId8bfd515b682c491785d2c5d933cc120a></span></p>
    412. 

  412. 

  413. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    414. 

  414. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【解析】</span></b></p>
    415. 

  415. 

  416. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    417. 

  417. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    418. 

  418. lang=EN-US>]</span></p>
    419. 

  419. 

  420. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    421. 

  421. vertical-align:middle'><span style='font-family:宋体'>由题意，数据按照从小到大的顺序排列，分析得</span><span
    422. 

  422. lang=EN-US><img width=20 height=19 src="test4.files/image030.png"
    423. 

  423. alt=eqIdd6c0e3ca15b3431487f3ef7f69c1d8a5></span><span style='font-family:宋体'>百分位数即为这组数据的中位数，所以找第</span><span
    424. 

  424. lang=EN-US><img width=13 height=17 src="test4.files/image032.png"
    425. 

  425. alt=eqIdddd35c5d043e4ebeac32a99367053c68></span><span style='font-family:宋体'>个数据</span><span
    426. 

  426. lang=EN-US><img width=24 height=19 src="test4.files/image031.png"
    427. 

  427. alt=eqId8bfd515b682c491785d2c5d933cc120a>.</span></p>
    428. 

  428. 

  429. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    430. 

  430. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    431. 

  431. lang=EN-US>]</span></p>
    432. 

  432. 

  433. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    434. 

  434. vertical-align:middle'><span style='font-family:宋体'>由题意可知，共有</span><span
    435. 

  435. lang=EN-US><img width=12 height=17 src="test4.files/image033.png"
    436. 

  436. alt=eqIdecb828cf922546bb9760e0ce5c95a9cb></span><span style='font-family:宋体'>个数据并且已经按照从小到大的顺序排列，其</span><span
    437. 

  437. lang=EN-US><img width=20 height=19 src="test4.files/image030.png"
    438. 

  438. alt=eqIdd6c0e3ca15b3431487f3ef7f69c1d8a5></span><span style='font-family:宋体'>百分位数即为这组数据的中位数，所以其</span><span
    439. 

  439. lang=EN-US><img width=20 height=19 src="test4.files/image030.png"
    440. 

  440. alt=eqIdd6c0e3ca15b3431487f3ef7f69c1d8a5></span><span style='font-family:宋体'>百分位数是第</span><span
    441. 

  441. lang=EN-US><img width=13 height=17 src="test4.files/image032.png"
    442. 

  442. alt=eqIdddd35c5d043e4ebeac32a99367053c68></span><span style='font-family:宋体'>个数据为</span><span
    443. 

  443. lang=EN-US><img width=24 height=19 src="test4.files/image031.png"
    444. 

  444. alt=eqId8bfd515b682c491785d2c5d933cc120a>.</span></p>
    445. 

  445. 

  446. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    447. 

  447. vertical-align:middle'><span style='font-family:宋体'>故答案为：</span><span
    448. 

  448. lang=EN-US><img width=24 height=19 src="test4.files/image031.png"
    449. 

  449. alt=eqId8bfd515b682c491785d2c5d933cc120a></span></p>
    450. 

  450. 

  451. <p class=MsoNormal><span lang=EN-US>&nbsp;</span></p>
    452. 

  452. 

  453. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题型】</span></b><b><span
    454. 

  454. style='font-family:宋体'>三、解答题</span></b></p>
    455. 

  455. 

  456. <p class=MsoNormal><b><span style='font-family:宋体;color:red'>【题干】</span></b></p>
    457. 

  457. 

  458. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    459. 

  459. vertical-align:middle'><b><span lang=EN-US>10</span></b><b><span
    460. 

  460. style='font-family:宋体'>、某环保组织进行了关于生态文明建设的知识竞赛，随机调查了</span><span lang=EN-US><img
    461. 

  461. width=27 height=19 src="test4.files/image034.png"
    462. 

  462. alt=eqId727650e20a234e51a97c72f164196d56></span></b><b><span style='font-family:
    463. 

  463. 宋体'>人，并统计了这</span><span lang=EN-US><img width=27 height=19
    464. 

  464. src="test4.files/image034.png" alt=eqId727650e20a234e51a97c72f164196d56></span></b><b><span
    465. 

  465. style='font-family:宋体'>人答对的题数，将统计数据分为</span><span lang=EN-US><img width=45
    466. 

  466. height=27 src="test4.files/image035.png"
    467. 

  467. alt=eqId0db6dcbbdf5a413399ed36fb7d1b351b></span></b><b><span style='font-family:
    468. 

  468. 宋体'>，</span><span lang=EN-US><img width=53 height=27
    469. 

  469. src="test4.files/image036.png" alt=eqIdac9f22de0f4642e1bfdb03fd1155a70d></span></b><b><span
    470. 

  470. style='font-family:宋体'>，</span><span lang=EN-US><img width=53 height=27
    471. 

  471. src="test4.files/image037.png" alt=eqIdef87905b72e94b538a64770e3c159b8c></span></b><b><span
    472. 

  472. style='font-family:宋体'>，</span><span lang=EN-US><img width=53 height=27
    473. 

  473. src="test4.files/image038.png" alt=eqId5311fffe69bd4b4aadcdbcbe62444c79></span></b><b><span
    474. 

  474. style='font-family:宋体'>，</span><span lang=EN-US><img width=60 height=27
    475. 

  475. src="test4.files/image039.png" alt=eqId26229bce05a94c028d8e6b6c471b9d6f></span></b><b><span
    476. 

  476. style='font-family:宋体'>，</span><span lang=EN-US><img width=62 height=24
    477. 

  477. src="test4.files/image040.png" alt=eqIdd82a617bb187424d9f7d34dcaad1460f></span></b><b><span
    478. 

  478. style='font-family:宋体'>六个小组，得到频率分布直方图如图所示．已知答对题数在</span><span lang=EN-US><img
    479. 

  479. width=53 height=27 src="test4.files/image038.png"
    480. 

  480. alt=eqId5311fffe69bd4b4aadcdbcbe62444c79></span></b><b><span style='font-family:
    481. 

  481. 宋体'>，</span><span lang=EN-US><img width=53 height=27
    482. 

  482. src="test4.files/image036.png" alt=eqIdac9f22de0f4642e1bfdb03fd1155a70d></span></b><b><span
    483. 

  483. style='font-family:宋体'>，</span><span lang=EN-US><img width=53 height=27
    484. 

  484. src="test4.files/image037.png" alt=eqIdef87905b72e94b538a64770e3c159b8c></span></b><b><span
    485. 

  485. style='font-family:宋体'>三组内对应的人数依次成等差数列．</span></b></p>
    486. 

  486. 

  487. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    488. 

  488. vertical-align:middle'><b><span lang=EN-US><img width=313 height=135
    489. 

  489. id="图片 100003" src="test4.files/image041.png" alt=figure></span></b></p>
    490. 

  490. 

  491. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    492. 

  492. vertical-align:middle'><b><span style='font-family:宋体'>（</span><span
    493. 

  493. lang=EN-US>1</span></b><b><span style='font-family:宋体'>）求频率分布直方图中</span><span
    494. 

  494. lang=EN-US><img width=14 height=14 src="test4.files/image042.png"
    495. 

  495. alt=eqId70a27b6ddf6b478285353abb3b1f3741></span></b><b><span style='font-family:
    496. 

  496. 宋体'>，</span><span lang=EN-US><img width=13 height=19
    497. 

  497. src="test4.files/image043.png" alt=eqIdaea992e70d4943e49e893817eb885ed7></span></b><b><span
    498. 

  498. style='font-family:宋体'>，并估计这</span><span lang=EN-US><img width=27 height=19
    499. 

  499. src="test4.files/image034.png" alt=eqId727650e20a234e51a97c72f164196d56></span></b><b><span
    500. 

  500. style='font-family:宋体'>人答对题数的中位数（精确到整数位）；</span></b></p>
    501. 

  501. 

  502. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    503. 

  503. vertical-align:middle'><b><span style='font-family:宋体'>（</span><span
    504. 

  504. lang=EN-US>2</span></b><b><span style='font-family:宋体'>）若答对题数属于</span><span
    505. 

  505. lang=EN-US><img width=45 height=27 src="test4.files/image044.png"
    506. 

  506. alt=eqId0786b511cc224ca2b6ffad852e2a586f></span></b><b><span style='font-family:
    507. 

  507. 宋体'>记为不合格，属于</span><span lang=EN-US><img width=59 height=27
    508. 

  508. src="test4.files/image045.png" alt=eqId0aa16512c21248b5a2bf711ac3f099ab></span></b><b><span
    509. 

  509. style='font-family:宋体'>记为优秀，现在要从不合格和优秀的人中用分层抽样的方法抽取</span><span lang=EN-US><img
    510. 

  510. width=12 height=19 src="test4.files/image046.png"
    511. 

  511. alt=eqId8f65c930571d4ff6aa6a50029d46826e></span></b><b><span style='font-family:
    512. 

  512. 宋体'>人，再从这</span><span lang=EN-US><img width=12 height=19
    513. 

  513. src="test4.files/image046.png" alt=eqId8f65c930571d4ff6aa6a50029d46826e></span></b><b><span
    514. 

  514. style='font-family:宋体'>人中随机抽取</span><span lang=EN-US><img width=13 height=17
    515. 

  515. src="test4.files/image047.png" alt=eqIdc052ddfbd4524f67a79e0e77c2e5656a></span></b><b><span
    516. 

  516. style='font-family:宋体'>人．求至少有</span><span lang=EN-US><img width=9 height=17
    517. 

  517. src="test4.files/image048.png" alt=eqId37705e1ef6a84bbdbe88433e75932cdf></span></b><b><span
    518. 

  518. style='font-family:宋体'>人为优秀的概率．</span></b></p>
    519. 

  519. 

  520. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    521. 

  521. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【知识点】</span></b></p>
    522. 

  522. 

  523. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    524. 

  524. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【难度】</span></b></p>
    525. 

  525. 

  526. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    527. 

  527. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【答案】</span></b><span
    528. 

  528. style='font-family:宋体'>（</span><span lang=EN-US>1</span><span style='font-family:
    529. 

  529. 宋体'>）</span><span lang=EN-US><img width=72 height=19
    530. 

  530. src="test4.files/image049.png" alt=eqIdce5bf3464fe141ef888c10ae02069f68></span><span
    531. 

  531. style='font-family:宋体'>，</span><span lang=EN-US><img width=72 height=19
    532. 

  532. src="test4.files/image050.png" alt=eqIdbb21945e11334c8aad1b97a8f09a1376></span><span
    533. 

  533. style='font-family:宋体'>，</span><span lang=EN-US>52</span><span
    534. 

  534. style='font-family:宋体'>；（</span><span lang=EN-US>2</span><span
    535. 

  535. style='font-family:宋体'>）</span><span lang=EN-US><img width=21 height=41
    536. 

  536. src="test4.files/image051.png" alt=eqId5255aa721623485f9dfbfd166a59c97a>.</span></p>
    537. 

  537. 

  538. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    539. 

  539. vertical-align:middle'><b><span style='font-family:宋体;color:red'>【解析】</span></b></p>
    540. 

  540. 

  541. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    542. 

  542. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>分析</span><span
    543. 

  543. lang=EN-US>]</span></p>
    544. 

  544. 

  545. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    546. 

  546. vertical-align:middle'><span style='font-family:宋体'>（</span><span lang=EN-US>1</span><span
    547. 

  547. style='font-family:宋体'>）由</span><span lang=EN-US><img width=53 height=27
    548. 

  548. src="test4.files/image038.png" alt=eqId5311fffe69bd4b4aadcdbcbe62444c79></span><span
    549. 

  549. style='font-family:宋体'>，</span><span lang=EN-US><img width=53 height=27
    550. 

  550. src="test4.files/image036.png" alt=eqIdac9f22de0f4642e1bfdb03fd1155a70d></span><span
    551. 

  551. style='font-family:宋体'>，</span><span lang=EN-US><img width=53 height=27
    552. 

  552. src="test4.files/image037.png" alt=eqIdef87905b72e94b538a64770e3c159b8c></span><span
    553. 

  553. style='font-family:宋体'>三组内对应的人数依次成等差数列，可得这三组对应的频率成等差数列，从而可得</span><span
    554. 

  554. lang=EN-US><img width=103 height=19 src="test4.files/image052.png"
    555. 

  555. alt=eqIdb2df192a08934088b3e22dc2f083e7c3></span><span style='font-family:宋体'>，再由各组的频率和为</span><span
    556. 

  556. lang=EN-US>1</span><span style='font-family:宋体'>，列方程组可求出</span><span
    557. 

  557. lang=EN-US><img width=14 height=14 src="test4.files/image042.png"
    558. 

  558. alt=eqId70a27b6ddf6b478285353abb3b1f3741></span><span style='font-family:宋体'>，</span><span
    559. 

  559. lang=EN-US><img width=13 height=19 src="test4.files/image043.png"
    560. 

  560. alt=eqIdaea992e70d4943e49e893817eb885ed7></span><span style='font-family:宋体'>，由于前</span><span
    561. 

  561. lang=EN-US>2</span><span style='font-family:宋体'>组的频率和小于</span><span lang=EN-US><img
    562. 

  562. width=24 height=19 src="test4.files/image053.png"
    563. 

  563. alt=eqId63bc1feb35174302ab3a170ffa50b1d0></span><span style='font-family:宋体'>，前</span><span
    564. 

  564. lang=EN-US>3</span><span style='font-family:宋体'>组的频率和大于</span><span lang=EN-US><img
    565. 

  565. width=24 height=19 src="test4.files/image054.png"
    566. 

  566. alt=eqId63bc1feb35174302ab3a170ffa50b1d0></span><span style='font-family:宋体'>，所以可知中位数在第</span><span
    567. 

  567. lang=EN-US>3</span><span style='font-family:宋体'>组，从而可求出中位数；</span></p>
    568. 

  568. 

  569. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    570. 

  570. vertical-align:middle'><span style='font-family:宋体'>（</span><span lang=EN-US>2</span><span
    571. 

  571. style='font-family:宋体'>）由分层抽样先计算出不合格的人数和优秀的人数，再利用列举法求概率</span></p>
    572. 

  572. 

  573. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    574. 

  574. vertical-align:middle'><span lang=EN-US>[</span><span style='font-family:宋体'>详解</span><span
    575. 

  575. lang=EN-US>]</span></p>
    576. 

  576. 

  577. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    578. 

  578. vertical-align:middle'><span style='font-family:宋体'>解：（</span><span lang=EN-US>1</span><span
    579. 

  579. style='font-family:宋体'>）由题意得</span><span lang=EN-US><img width=217 height=27
    580. 

  580. src="test4.files/image055.png" alt=eqId0cdd84cd95614d1db66f30c3e2d0cdc8></span><span
    581. 

  581. style='font-family:宋体'>，解得</span><span lang=EN-US><img width=72 height=19
    582. 

  582. src="test4.files/image049.png" alt=eqIdce5bf3464fe141ef888c10ae02069f68></span><span
    583. 

  583. style='font-family:宋体'>，</span></p>
    584. 

  584. 

  585. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    586. 

  586. vertical-align:middle'><span style='font-family:宋体'>又</span><span lang=EN-US><img
    587. 

  587. width=153 height=19 src="test4.files/image056.png"
    588. 

  588. alt=eqIddbeb42d887dc40b88fe0c07cb29101ab></span><span style='font-family:宋体'>，</span><span
    589. 

  589. lang=EN-US><img width=15 height=13 src="test4.files/image057.png"
    590. 

  590. alt=eqId6f7ed67c0a024364806a23a71f56aeb5><img width=72 height=19
    591. 

  591. src="test4.files/image050.png" alt=eqIdbb21945e11334c8aad1b97a8f09a1376></span><span
    592. 

  592. style='font-family:宋体'>．</span></p>
    593. 

  593. 

  594. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    595. 

  595. vertical-align:middle'><span lang=EN-US><img width=161 height=27
    596. 

  596. src="test4.files/image058.png" alt=eqIdde3519eecf1b482982ed63556318087e></span><span
    597. 

  597. style='font-family:宋体'>，所以中位数大约是</span><span lang=EN-US><img width=113
    598. 

  598. height=41 src="test4.files/image059.png"
    599. 

  599. alt=eqIdcc19018fa38240979c166087aefb7277></span><span style='font-family:宋体'>．</span></p>
    600. 

  600. 

  601. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    602. 

  602. vertical-align:middle'><span style='font-family:宋体'>（</span><span lang=EN-US>2</span><span
    603. 

  603. style='font-family:宋体'>）不合格的人数为：</span><span lang=EN-US><img width=212
    604. 

  604. height=27 src="test4.files/image060.png"
    605. 

  605. alt=eqId23210575dc4f464290e05df766ba643c></span><span style='font-family:宋体'>，</span></p>
    606. 

  606. 

  607. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    608. 

  608. vertical-align:middle'><span style='font-family:宋体'>优秀的人数为：</span><span
    609. 

  609. lang=EN-US><img width=213 height=27 src="test4.files/image061.png"
    610. 

  610. alt=eqId3579fac6580d47c1adc382f76719f35b></span><span style='font-family:宋体'>，</span></p>
    611. 

  611. 

  612. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    613. 

  613. vertical-align:middle'><span style='font-family:宋体'>所以</span><span lang=EN-US>“</span><span
    614. 

  614. style='font-family:宋体'>优秀</span><span lang=EN-US>”</span><span
    615. 

  615. style='font-family:宋体'>抽取</span><span lang=EN-US><img width=59 height=41
    616. 

  616. src="test4.files/image062.png" alt=eqId05fb2711f33f49dba48a471864797adb></span><span
    617. 

  617. style='font-family:宋体'>人，</span></p>
    618. 

  618. 

  619. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    620. 

  620. vertical-align:middle'><span lang=EN-US>“</span><span style='font-family:宋体'>不合格</span><span
    621. 

  621. lang=EN-US>”</span><span style='font-family:宋体'>抽取</span><span lang=EN-US><img
    622. 

  622. width=57 height=41 src="test4.files/image063.png"
    623. 

  623. alt=eqId37de7c8668314034bfba4321570bbb81></span><span style='font-family:宋体'>人，</span></p>
    624. 

  624. 

  625. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    626. 

  626. vertical-align:middle'><span style='font-family:宋体'>设两名</span><span lang=EN-US>“</span><span
    627. 

  627. style='font-family:宋体'>优秀</span><span lang=EN-US>”</span><span
    628. 

  628. style='font-family:宋体'>的人记为：</span><span lang=EN-US><img width=19 height=24
    629. 

  629. src="test4.files/image064.png" alt=eqIde660daa143d5431e96530c61b610d572></span><span
    630. 

  630. style='font-family:宋体'>，</span><span lang=EN-US><img width=20 height=24
    631. 

  631. src="test4.files/image065.png" alt=eqId01ad4ec8cf0543da939adaa52264b614></span><span
    632. 

  632. style='font-family:宋体'>，三名</span><span lang=EN-US>“</span><span
    633. 

  633. style='font-family:宋体'>不合格</span><span lang=EN-US>”</span><span
    634. 

  634. style='font-family:宋体'>的人记为：</span><span lang=EN-US><img width=15 height=24
    635. 

  635. src="test4.files/image066.png" alt=eqId91527d9f559f45afb12460e0c2e33b6f></span><span
    636. 

  636. style='font-family:宋体'>，</span><span lang=EN-US><img width=16 height=24
    637. 

  637. src="test4.files/image067.png" alt=eqId802dd8e915624120aa727fb9b14978b0></span><span
    638. 

  638. style='font-family:宋体'>，</span><span lang=EN-US><img width=16 height=24
    639. 

  639. src="test4.files/image068.png" alt=eqId366cae234e024c18a9452147867e83c8></span><span
    640. 

  640. style='font-family:宋体'>，</span></p>
    641. 

  641. 

  642. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    643. 

  643. vertical-align:middle'><span style='font-family:宋体'>则这</span><span lang=EN-US><img
    644. 

  644. width=12 height=19 src="test4.files/image046.png"
    645. 

  645. alt=eqId8f65c930571d4ff6aa6a50029d46826e></span><span style='font-family:宋体'>人中任选</span><span
    646. 

  646. lang=EN-US><img width=13 height=17 src="test4.files/image047.png"
    647. 

  647. alt=eqIdc052ddfbd4524f67a79e0e77c2e5656a></span><span style='font-family:宋体'>人有：</span><span
    648. 

  648. lang=EN-US><img width=53 height=27 src="test4.files/image069.png"
    649. 

  649. alt=eqIdbdb17c9ce86b4373b7e20b712eca07c8></span><span style='font-family:宋体'>，</span><span
    650. 

  650. lang=EN-US><img width=51 height=27 src="test4.files/image070.png"
    651. 

  651. alt=eqIdc99026a42d774c7987857f1b585ed510></span><span style='font-family:宋体'>，</span><span
    652. 

  652. lang=EN-US><img width=49 height=27 src="test4.files/image071.png"
    653. 

  653. alt=eqId9ceae128c22c4d5a92ba4ba300efa8aa></span><span style='font-family:宋体'>，</span><span
    654. 

  654. lang=EN-US><img width=49 height=27 src="test4.files/image072.png"
    655. 

  655. alt=eqIdf5d4e896cb33451a9dc9dc8802ee84b9></span><span style='font-family:宋体'>，</span><span
    656. 

  656. lang=EN-US><img width=51 height=27 src="test4.files/image073.png"
    657. 

  657. alt=eqId126d5d6c34164da495848b60770abd8b></span><span style='font-family:宋体'>，</span><span
    658. 

  658. lang=EN-US><img width=52 height=27 src="test4.files/image074.png"
    659. 

  659. alt=eqIdc0f7020952c14a18adb768e344154a88></span><span style='font-family:宋体'>，</span><span
    660. 

  660. lang=EN-US><img width=52 height=27 src="test4.files/image075.png"
    661. 

  661. alt=eqIdd1418fa81f0942b5b00be80918723ad5></span><span style='font-family:宋体'>，</span><span
    662. 

  662. lang=EN-US><img width=48 height=27 src="test4.files/image076.png"
    663. 

  663. alt=eqId7253f291a94f4b13b06764079db5bde1></span><span style='font-family:宋体'>，</span><span
    664. 

  664. lang=EN-US><img width=47 height=27 src="test4.files/image077.png"
    665. 

  665. alt=eqId09fa812d6c9f4fcca407ddfd7fa870b3></span><span style='font-family:宋体'>，</span><span
    666. 

  666. lang=EN-US><img width=48 height=27 src="test4.files/image078.png"
    667. 

  667. alt=eqIdbbc713519b514dd3a8f36d81a4c717ac></span><span style='font-family:宋体'>共</span><span
    668. 

  668. lang=EN-US><img width=19 height=19 src="test4.files/image079.png"
    669. 

  669. alt=eqId62503849440740cf8754af7e844ba72c></span><span style='font-family:宋体'>种情形，至少有</span><span
    670. 

  670. lang=EN-US><img width=9 height=17 src="test4.files/image048.png"
    671. 

  671. alt=eqId37705e1ef6a84bbdbe88433e75932cdf></span><span style='font-family:宋体'>人为优秀有：</span></p>
    672. 

  672. 

  673. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    674. 

  674. vertical-align:middle'><span lang=EN-US><img width=53 height=27
    675. 

  675. src="test4.files/image069.png" alt=eqIdbdb17c9ce86b4373b7e20b712eca07c8></span><span
    676. 

  676. style='font-family:宋体'>，</span><span lang=EN-US><img width=51 height=27
    677. 

  677. src="test4.files/image070.png" alt=eqIdc99026a42d774c7987857f1b585ed510></span><span
    678. 

  678. style='font-family:宋体'>，</span><span lang=EN-US><img width=49 height=27
    679. 

  679. src="test4.files/image071.png" alt=eqId9ceae128c22c4d5a92ba4ba300efa8aa></span><span
    680. 

  680. style='font-family:宋体'>，</span><span lang=EN-US><img width=49 height=27
    681. 

  681. src="test4.files/image072.png" alt=eqIdf5d4e896cb33451a9dc9dc8802ee84b9></span><span
    682. 

  682. style='font-family:宋体'>，</span><span lang=EN-US><img width=51 height=27
    683. 

  683. src="test4.files/image073.png" alt=eqId126d5d6c34164da495848b60770abd8b></span><span
    684. 

  684. style='font-family:宋体'>，</span><span lang=EN-US><img width=52 height=27
    685. 

  685. src="test4.files/image074.png" alt=eqIdc0f7020952c14a18adb768e344154a88></span><span
    686. 

  686. style='font-family:宋体'>，</span><span lang=EN-US><img width=52 height=27
    687. 

  687. src="test4.files/image075.png" alt=eqIdd1418fa81f0942b5b00be80918723ad5></span><span
    688. 

  688. style='font-family:宋体'>，共有</span><span lang=EN-US>7</span><span
    689. 

  689. style='font-family:宋体'>种，</span></p>
    690. 

  690. 

  691. <p class=MsoNormal align=left style='text-align:left;line-height:150%;
    692. 

  692. vertical-align:middle'><span style='font-family:宋体'>因此至少有</span><span
    693. 

  693. lang=EN-US><img width=9 height=17 src="test4.files/image048.png"
    694. 

  694. alt=eqId37705e1ef6a84bbdbe88433e75932cdf></span><span style='font-family:宋体'>人为优秀的概率为</span><span
    695. 

  695. lang=EN-US><img width=48 height=41 src="test4.files/image080.png"
    696. 

  696. alt=eqId2246d42901ea4089ae938060212b113b></span><span style='font-family:宋体'>．</span></p>
    697. 

  697. 

  698. </div>
    699. 

  699. 

  700. </body>
    701. 

  701. 

  702. </html>
    703. 

  703.